Velocity and Entropy of Motion in Periodic Potentials

Andreas Knauf[1]

  • [1] Max-Planck-Institut für Math. in den Naturw., Inselstr. 22–26, D-04103 Leipzig, Germany

Séminaire Équations aux dérivées partielles (1996-1997)

  • Volume: 1996-1997, page 1-11

Abstract

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This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.

How to cite

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Knauf, Andreas. "Velocity and Entropy of Motion in Periodic Potentials." Séminaire Équations aux dérivées partielles 1996-1997 (1996-1997): 1-11. <http://eudml.org/doc/10921>.

@article{Knauf1996-1997,
abstract = {This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.},
affiliation = {Max-Planck-Institut für Math. in den Naturw., Inselstr. 22–26, D-04103 Leipzig, Germany},
author = {Knauf, Andreas},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Velocity and Entropy of Motion in Periodic Potentials},
url = {http://eudml.org/doc/10921},
volume = {1996-1997},
year = {1996-1997},
}

TY - JOUR
AU - Knauf, Andreas
TI - Velocity and Entropy of Motion in Periodic Potentials
JO - Séminaire Équations aux dérivées partielles
PY - 1996-1997
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1996-1997
SP - 1
EP - 11
AB - This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.
LA - eng
UR - http://eudml.org/doc/10921
ER -

References

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  1. Asch, J., Knauf, A.: Motion in Periodic Potentials. Preprint (1997) Zbl0896.34027MR1492956
  2. Benatti, F., Hudetz, T., Knauf, A.: Quantum Chaos and Dynamical Entropy. Preprint (1997) Zbl0927.37008MR1670033
  3. Connes, A., Narnhofer, H., Thirring, W.: Dynamical Entropy for C* algebras and von Neumann Algebras. Commun. Math. Phys. 112, 691 (1987). Zbl0637.46073MR910587
  4. Gérard, Ch., Nier, F.: Scattering Theory for the Perturbations of Periodic Schrödinger Operators. Preprint Ecole Polytechnique (1997) Zbl0934.35111MR1669979
  5. Klein, M., Knauf, A.: Classical Planar Scattering by Coulombic Potentials. Lecture Notes in Physics m 13. Berlin, Heidelberg, New York: Springer; 1993 Zbl0783.70001
  6. Knauf, A.: Ergodic and Topological Properties of Coulombic Periodic Potentials. Commun. Math. Phys. 110, 89–112 (1987) Zbl0616.58044MR885572
  7. Knauf, A.: Coulombic Periodic Potentials: The Quantum Case. Annals of Physics 191, 205–240 (1989) MR1003009
  8. Knauf, A.: Closed orbits and converse KAM theory. Nonlinearity 3, 961–973 (1990) Zbl0702.70013MR1067089
  9. Reed, M., Simon, B.: Methods in Mathematical Physics, Vol. IV: Analysis of Operators. New York: Academic Press 1978 Zbl0401.47001MR493421
  10. Thomas, L.E.: Time Dependent Approach to Scattering from Impurities in a Crystal. Commun. Math. Phys 33, 335–343 (1973) MR334766

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